Related papers: How robust is quicksort average complexity?

Studying the robustness of machine learning models is important to ensure consistent model behaviour across real-world settings. To this end, adversarial robustness is a standard framework, which views robustness of predictions through a…

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…

Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each…

The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…

We provide a smoothed analysis of Hoare's find algorithm and we revisit the smoothed analysis of quicksort. Hoare's find algorithm - often called quickselect - is an easy-to-implement algorithm for finding the k-th smallest element of a…

As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…

Sorting is one of the oldest computing problems and is still very important in the age of big data. Various algorithms and implementation techniques have been proposed. In this study, we focus on comparison based, internal sorting…

Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…

To address the shortcomings of real-world datasets, robust learning algorithms have been designed to overcome arbitrary and indiscriminate data corruption. However, practical processes of gathering data may lead to patterns of data…

Reliable probabilistic primality tests are fundamental in public-key cryptography. In adversarial scenarios, a composite with a high probability of passing a specific primality test could be chosen. In such cases, we need worst-case error…

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…

Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…

We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending…

The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on…

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small…

We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…

Despite the vast success of Deep Neural Networks in numerous application domains, it has been shown that such models are not robust i.e., they are vulnerable to small adversarial perturbations of the input. While extensive work has been…